Faddeev-Reshetikhin model from a 4D Chern-Simons theory

Fukushima, Osamu; Sakamoto, Jun-ichi; Yoshida, Kentaroh

doi:10.1007/jhep02(2021)115

Cited by 20 publications

(9 citation statements)

References 10 publications

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“…The coupling to the B-field is different from the usual YB deformation, and so the other components like R-R fields and dilaton other than the metric would be modified due to the appearance of the new ingredient Σ . We will report some results in another place [23].…”

Section: Conclusion and Discussionmentioning

confidence: 91%

Comments on $η$-deformed principal chiral model from 4D Chern-Simons theory

Fukushima,

Sakamoto,

Yoshida

2020

Preprint

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We study η-deformations of principal chiral model (PCM) from the viewpoint of a 4D Chern-Simons (CS) theory. The η-deformed PCM has originally been derived from the 4D CS theory by Delduc, Lacroix, Magro and Vicedo [arXiv:1909.13824]. The derivation is based on a twist function in the rational description. On the other hand, we start with a twist function in the trigonometric description and discuss possible boundary conditions. We show that a certain boundary condition reproduces the usual η-deformed PCM and another one leads to a new kind of Yang-Baxter deformation.

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Section: Conclusion and Discussionmentioning

confidence: 91%

Comments on $η$-deformed principal chiral model from 4D Chern-Simons theory

Fukushima,

Sakamoto,

Yoshida

2020

Preprint

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“…The 4-dimensional gauge theoretic origin of 2-dimensional integrable field theories, as proposed by Costello and Yamazaki in [CY], has been extensively studied over the past couple of years, see for instance [DLMV3,Sc1,FSY1,FSY2,CS,T,THC,BSV,BS,LV,CSV,FSY3,ABW,FSY4,D,St,Sc2,L2,FSY5].…”

Section: Quantum Gaudin Modelsmentioning

confidence: 99%

3-dimensional mixed BF theory and Hitchin's integrable system

Vicedo,

Winstone

2022

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The affine Gaudin model, associated with an untwisted affine Kac-Moody algebra, is known to arise from a certain gauge fixing of 4-dimensional mixed topological-holomorphic Chern-Simons theory in the Hamiltonian framework. We show that the finite Gaudin model, associated with a finite-dimensional semisimple Lie algebra, or more generally the tamely ramified Hitchin system on an arbitrary Riemann surface, can likewise be obtained from a similar gauge fixing of 3-dimensional mixed BF theory in the Hamiltonian framework.

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“…In this new approach, the two dimensional integrable field theories can be systematically constructed by inserting two dimensional defects into a novel four dimensional(4D) Chern-Simons (4DCS) theory [4] which is specified by a holomorphic 1-form ω, generalizing the study on lattice integrable models in [5][6][7]. This 4D gauge theory approach has attracted much attention and has been under intense study since its proposal [9][10][11][12][13][14][15][16][17][18][19][20][21].…”

Section: Introductionmentioning

confidence: 99%

Deformed Integrable Models from Holomorphic Chern-Simons Theory

Chen,

He,

Tian

2021

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We study the approaches to two-dimensional integrable field theories via a sixdimensional(6D) holomorphic Chern-Simons theory defined on twistor space. Under symmetry reduction, it reduces to a four-dimensional Chern-Simons theory, while under solving along fibres it leads to four-dimensional(4D) integrable theory, the anti-self-dual Yang-Mills or its generalizations. From both four-dimensional theories, various two-dimensional integrable field theories can be obtained. In this work, we try to investigate several twodimensional integrable deformations in this framework. We find that the λ-deformation, the rational η-deformation and the generalized λ-deformation can not be realized from 4D integrable model approach, even though they could be obtained from 4D Chern-Simons theory. The obstacle stems from the incompatibility between the symmetry reduction and the boundary conditions. Nevertheless, we show that a coupled theory of λ-deformation and the η-deformation in the trigonometric description could be obtained from the 6D theory in both ways, by considering the case that (3, 0)-form in the 6D theory is allowed to have zeros. 1 Introduction 1 2 Integrable field theories from holomorphic Chern-Simons theory 3 2.1 Holomorphic Chern-Simons on twistor space 3 2.2 Symmetry reduction to 4D Chern-Simons theory 5 2.3 Solving the 4D CS theory reduced from holomorphic Chern-Simons 7 2.4 Solving along fibres for holomorphic Chern-Simons theory 8 2.5 Symmetry reduction to 2D theory 9 3 λ-deformed principal chiral model from holomorphic Chern-Simons 10 3.1 Solving the 4D CS theory reduced from holomorphic Chern-Simons 11 3.2 Boundary conditions for holomorphic Chern-Simons theory 13 3.3 Solving along fibres for holomorphic Chern-Simons theory 13 4 Other possible deformations 15 4.1 η-deformation 15 4.2 Generalized λ-deformation 17 5 Coupled λ-deformation: an example with a fourth-order pole 19 6 η-deformation from the trigonometric description 22 6.1 Solving along fibres for holomorphic Chern-Simons theory 23 6.2 Symmetry reduction to 2D theory 26 6.3 Symmetry reduction of 6DhCS to 4D Chern-Simons theory 27 7 Conclusions 30

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Faddeev-Reshetikhin model from a 4D Chern-Simons theory

Cited by 20 publications

References 10 publications

Comments on $η$-deformed principal chiral model from 4D Chern-Simons theory

Comments on $η$-deformed principal chiral model from 4D Chern-Simons theory

3-dimensional mixed BF theory and Hitchin's integrable system

Deformed Integrable Models from Holomorphic Chern-Simons Theory

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